This Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program (CFDA 47.070) provides $600,000 to Carnegie Mellon University (CMU) to conduct collaborative research on using machine learning to solve partial differential equations (PDEs) and leverage PDEs for generative modeling. The project aims to explore the representational power, inductive biases, statistical complexity, and numerical stability of different neural architectures for PDE solving, as well as the tradeoffs of PDE-based generative models. Researchers at CMU will leverage their expertise in mathematical foundations of PDEs and generative modeling, as well as numerical optimization, to advance the synergy between PDEs and machine learning. The award has an anticipated completion date of July 31, 2028.
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